I wouldn’t recommend The LaTeX Companion to new users. Once you’ve got your feet wet, it’s very handy (although most everything in it can be found in the documentation on your system), but I think it would really confuse people who didn’t understand the basics.

What about Lamport’s book, which covers the basics? Or Gratzer’s More Math into LaTeX? I edited the third edition of Gratzer’s Math into LaTeX, so I might be a bit biased (although I don’t see a penny from any sales), but I think that it and the new edition do the best job of getting people up to speed on serious math of any book I’ve seen, with an introductory “writing your first article” bit and then more advanced chapters covering more advanced mathematical typesetting, basic macro programming, and more. The new edition also covers getting a TeX system installed, picking an editor, and other useful information for getting started.